Chapter 6. Compact Multimode Interference Couplers with Arbitrary
6.5 Transfer functions of half MMI-D
According to conditions for a overlapping-image MMI coupler as mentioned in early and referring to Fig. 6.6(b), MMI-hD with a section having length = (3/10)LπD corresponding to N = 10 has 9 possible input/output locations for self-images. When i = 2 and 6, we have a (14 : 36 : 36 : 14) and a (36 : 14 : 14 : 36) MMI coupler as shown in Fig. 6.18(a) and (b), respectively. For analysis of the cascading MMI by MMI-hD + MMI-E as case indicated in Fig. 6.10(d), first, we should examine the transfer functions of MMI-hD by Eq. (6.5) and summarize them in Table 6-2. Then, the transfer matrix of this cascaded device can be obtained by the following matrix multiplication.
(6.13)
where HX and E HBE of MMI-E have the same phase relationship as MMI-A. Therefore, we yield HXEhD 2 = 2760. and HBEhD2 =0.724.
Fig. 6.18. The simulated 2-D field maps for half of MMI-D (MMI-hD): (a) when i = 2, power splitter ratio = 14 : 36 : 36 : 14, (b) when i = 6, power splitter ratio = 36 : 14 : 14 : 36.
Table 6-2 Transfer functions of MMI-hD
Reference
[6.1] L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol., vol. 13, no. 4, pp. 615-627, 1995.
[6.2] D. G. Rabus, M. Hamacher, U. Troppenz, and H. Heidrich, “Optical filters based on ring resonators with integrated semiconductor optical amplifiers in GaInAsP-InP,”
IEEE J. Sel. Topics Quantum Electron., vol. 8, pp. 1405-1411, 2002.
[6.3] G. Lenz and C. K. Madsen, “General optical all-pass filter structures for dispersion control in WDM systems,” J. Lightwave Technol., vol. 17, pp. 1248-1254, 1999.
[6.4] S. Suzuki, K. Oda, and Y. Hibino, “Integrated-optic double-ring resonators with a wide free spectral range of 100 GHz,” J. Lightwave Technol., vol. 13, pp. 1766-1770, 1995.
[6.5] S. Matsuo, Y. Yoshikuni, T. Segawa, Y. Ohiso, and H. Okamoto, “A widely tunable optical filter using ladder-type structure,” IEEE Photon. Technol. Lett., vol. 15, pp.
1114-1116, 2003.
[6.6] V. M. Menon, W. Tong, C. Li, F. Xia, I. Glesk, P. R. Prucnal, and S. R. Forrest,
“All-optical wavelength conversion using a regrowth-free monolithically integrated Sagnac interferometer,” IEEE Photon. Technol. Lett., vol. 15, pp. 254-256, 2003.
[6.7] M. G. Kane, I. Glesk, J. P. Sokoloff, and P. R. Prucnal, “Asymmetric optical loop mirror: analysis of an all-optical switch,” Appl. Opt., vol. 33, pp. 6833-6842, 1994.
[6.8] D. B. Mortimore, “Fiber loop reflectors,” J. Lightwave Technol., vol. 6, pp.
1217-1224, 1988.
[6.9] M. Bachmann, P. A. Besse, and H. Melchior, “Overlapping-image multimode interference couplers with a reduced number of self-images for uniform and nonuniform power splitting,” Appl. Opt., vol. 34, pp. 6898-6910, 1995.
[6.10] J. Leuthold and C. H. Joyner, “Multimode interference couplers with tunable power splitting ratios,” J. Lightwave Technol., vol. 19, pp. 700-707, 2001.
[6.11] P. A. Besse, E. Gini, M. Bachmann, and H. Melchior. “New 2x2 and 1x3 Multimode Interference Couplers with Free Selection of Power Splitting Ratios,” J. Lightwave Technol., vol. 14, pp. 2286-2293, 1996.
[6.12] N. S. Lagali, M. R. Paiam, and R. I. MacDonald, “Theory of variable-ratio power splitters using multimode interference couplers,” IEEE Photonics Technol. Lett. vol.
11, pp. 665-667, 1999.
[6.13] H. Ohe, H. Shimizu, and Y. Nakano, “InGaAlAs multiple-quantum-well optical phase modulators based on carrier depletion,” IEEE Photon. Technol. Lett., vol. 19, pp. 1816-1818, 2007.
[6.14] Q. Lai, M. Bachmann, W. Hunziker, P. A. Besse, and H. Melchior, “Arbitrary ratio power splitters using angled silica on silicon multimode interference couplers,”
Electron. Lett., vol. 32, pp. 1576-1577, 1996.
[6.15] D. S. Levy, Y. M. Li, R. Scarmozzino, and R. M. Osgood Jr. “A multimode interference-based variable power splitter in GaAs-AlGaAs,” IEEE Photon. Technol.
Lett., vol. 9, pp. 1373-1375, 1997.
[6.16] T. Saida, A. Himeno, M. Okuno, A. Sugita, and K. Okamoto, “Silica-based 2x2 multimode interference coupler with arbitrary power splitting ratio,” Electron. Lett., vol. 35, pp. 2031-2033, 1999.
[6.17] S. Y. Tseng, C. F. Hernandez, D. Owens, and B. Kippelen, “Variable splitting ratio 2×2 MMI couplers using multimode waveguide holograms,” Opt. Express, vol. 15, pp. 9015-9021, 2007.
[6.18] David J. Y. Feng, P. Y. Chang, T. S. Lay, and T. Y. Chang, “Novel stepped-width design concept for compact multimode-interference couplers with low cross-coupling ratio,” IEEE Photon. Technol. Lett., vol. 19, pp. 224-226, 2007.
[6.19] David J. Y. Feng, T. S. Lay, and T. Y. Chang, “Waveguide couplers with new power splitting ratios made possible by cascading of short multimode interference sections,”
Opt. Express, vol. 15, pp. 1588-1593, 2007.
[6.20] C. J. Kaalund and Z. Jin, “Novel multimode interference devices for low index contrast materials systems featuring deeply etched air trenches,” Opt. Commun., vol.
250, pp. 292-296, 2005.
[6.21] A. S. Sudbo, “Film mode matching: a versatile numerical method for vector mode field calculations in dielectric waveguides,” Pure App. Opt., vol. 2, pp. 211-233, 1993.
[6.22] S. Sudbo, “Improved formulation of the film mode matching method for mode field calculations in dielectric waveguides,” Pure App. Opt., vol. 3, pp. 381-388, 1994.
[6.23] FimmProp, version 4.3, Photon Design, Oxford, U.K., 2004.
[6.24] BeamPROP, version 5.1, RSoft Inc., NY, 2005.
[6.25] R. M. Knox and P. P. Toulios, “Integrated circuits for millimiter through optical frequency range,” in Proc. Symp. Submillimiter Waves, J. Fox, Ed., New York,
Mar./Apr. 1970, pp. 497-516.
[6.26] M. Bachmann, P. A. Besse, and H. Melchior, “General self-imaging properties in NxN multimode interference couplers including phase relations,” Appl. Opt., vol. 33, pp. 3950-3911, 1994.
Chapter 7
Summary
Efforts to realize high-performance multi-function InGaAlAs laser/SOAs on InP substrate have been discussed in previous chapters. In addition, compact waveguide couplers achieving arbitrary power splitting ratio are also exposed. The key accomplishments and important improvement for materials and waveguide devices of this research are summarized as follows:
For materials:
● Based on those confident band structure parameters of binary compounds (Table A-1 and A-2) with the band-lineup method presented in Appendix-A, which important quantities of achievable strained ternary/quaternary InGa(Al)As alloys (Appendix-B) were applied on designing the strained InGaAs/InGaAlAs multiple quantum wells laser/SOAs structures. The quantum well contains a lattice-matched InGaAs core, a compressive-strained InGaAs padding, and a tensile-strained InGaAlAs spacer.
Strain-balanced triple-QWs structure are designed to incorporate all attractive features discussed in Chapter-1 as a compromise between threshold current, differential gain and Δn. With our optimum design, a 5.2-nm thick and strain-compensated QWs can achieve a high value of wavefunction OIS of 0.94 for e1-hh1 emission wavelength at 1.55 μm.
● With a stable growth procedure (Appendix-D) and cell-flux calibration method (Chapter-3), the technique of growing high quality InGaAlAs/InAlAs/InGaAs materials on InP substrate by solid-source MBE technology has been established.
● MBE-grown InGaAlAs bulk and QWs samples are extensively characterized by double-crystal X-ray diffraction (DCXRD) and transmission electron microscopy (TEM). In particular, the simulated X-ray diffraction result is consistent with the experimental one (See Fig. 3.13). It means the layer composition and thickness can be precisely controlled. Furthermore, TEM pictures from two different cross-section, (0-11) and (011), demonstrate that no point defects, dislocation, or quantum dot/wire exist within our samples.
● In addition, interband transitions in strained MQWs have been investigated by photoluminescence (PL), electroluminescence (EL), and photocurrent spectra measurements (Chapter- 4 and Chapter-5).
● For λ = 1.55 μm samples, ridge-waveguide lasers of Fabry-Perot (FP) type and tilted-end-facet (TEF) type were fabricated by a new developed multi-step wet-etching process (Section 4.2). When injection current density > 20A/cm2,EL spectra show higher optical gain for the e1-hh2 transition at λ = 1460 nm than the e1-hh1 transition at λ = 1550 nm. The FP laser shows a lasing peak of λ = 1514 nm at threshold. Additional lasing wavelength at λ =1528 nm and 1545 nm were observed sequentially as the injection current increased. However, for the TEF laser, only the emission at λ = 1511 nm was observed. These TE-polarized lasing wavelengths are consistent with the δ-like absorption peaks in photocurrent spectra. Because our modulation-doped strained MQWs structure could cause the strain-field profile and alloy segregation/migration, therefore, the lasing performance is possible attributed to optical transitions similar to quantum dots/wires, which structure had been demonstrated that laser can be operated at excited transitions.
● Another six blue-shift samples (λ = 1.48 μm) were prepared for investigating which design can offer a high chirp parameter (Δn/Δk). S4 with n-type modulation-doping amounting to a sheet density of 3.5 × 1011 cm-2 per QW and combining with a hole-stopping barrier represents the largest chirp parameter under reversed bias (Fig.
5.14), which offers an excellent platform to realize electro-refractive devices with larger refractive index changes (Δn) but lower differential absorption (Δα) near λ = 1.55 μm, which is also our interested region of operation.
For waveguide devices:
● We have succeeded in reducing the length of conventional constant-width multimode interference (MMI) coupler of K = 0.15 and 0.28 more than 32% by a novel stepped-width design concept. With this design, according to wavelength dependence simulation, their 1-dB bandwidth of K = 0.15 and 0.28 can be separately extended to 86-nm and 61-nm from 49-nm and 39-nm.
● By extending the stepped-with idea, we show that it is possible to obtain 2×2 waveguide couplers with new power splitting ratios of 7%, 64%, 80% and 93% for cross coupling by cascading two short MMI sections.
● Based on those basic transfer functions of relative short MMI sections with using matrix multiplication of Eq. (6.6), we have examined the results of all possible combinations as summarized in Fig. 6.12 and verified their consistency with the results of 3-D BPM simulations.
● We further realize freely chosen power splitting ratio by interconnecting a pair of unequal-width waveguides as the phase-tuning section into the middle of two short
MMI sections. Due to the compact and low loss MMI-based devices using only rectangular geometry without any bent, curved, and tapered waveguides involved, the final K value obtained by this kind of MMI coupler will be not so sensitivity to the typical mask resolution and photolithography process variability. They offer valuable new possibilities for designing waveguide-based photonic integrated circuits (PIC’s).
In conclusion, this work is focused on developing a multi-function material and a way to size down waveguide coupler devices. However, more key issues should be taken into consideration for achieving a complicated waveguide-based PIC’s, such as how to reduce material absorption in passive waveguide region (QWI process) and how to isolate the electrical bias between active and passive device (high resistivity materials, low-temperature regrowth).
Therefore, this work should be regarded as the one of preparation for developing SOA-based PIC’s.
On the other hand, based on our designed samples, a PIC’s device for wavelength addressable, called as ring-resonator loop-mirror laser, is also under investigated and discussed in Appendix-E.
Appendix - A
Band Lineup and Effective Mass of Strained Layers
In order to determine the material properties in strained quantum well, we must know how to align the band diagram and estimate their effective mass first. In this appendix, we present a universal method for important quantities in coherently strained alloys. The most important thing to exactly calculate the band lineups between strained materials is to achieve a precise bandgap of alloys. In section A.1.1, alloy’s bandgap, as usual, is regarded as an unstrained bulk material, and calculated with consideration of the ternary and quaternary bowing parameters. With considering the strain effect, the strained bandgap and band offset are following introduced in section A.1.2. Then, the band alignment procedure is finally done by Harrison model [A1] as presented in section A.2.3. Also, the way to obtain the effective mass with strain is reported in section A.1.4. Because three Group-III elements (In, Ga, Al) with two Group-V (As, P) ones are simultaneously involved to introduce those important quantities for coherently strained alloys, in Section A.1, it is thus quite useful for material systems of InGaAs on GaAs, InGaAsP on InP, and InGaAlAs on InP. Based on Section A.1, the characteristics of InGaAlAs strained alloys on InP are specially discussed in Section A.2.
A.1 Important quantities for coherently strained In1-x-yGaxAlyAszP1-z --- Unstrained bandgap, strained bandgap, band offset and effective mass
A.1.1 Unstrained direct bandgaps of alloy compounds, Egu , are given as (accuracy is lower when both Al and P are present)
gu 1-x-y x y z 1-z The values of physical parameter of the binary semiconductor used here according to the recommended ones by Vurgaftman et al (2001) [A2] can be found in Table A-1. Which ternary and quaternary bowing parameters for unstrained bandgap are given by Table A-2.
A.1.2 Biaxial strain
When there is lattice mismatch between the epi-layer and the substrate, the epi-layer becomes biaxially strained. If the lattice constant becomes a0 ≠ au and the growth is pseudomorphic (no dislocations), i.e. the in-plane (xy) lattice distance of epi-layer is equal to one of the substrate (GaAs or InP), the amount of in-plane strain is defined as
0
where au is the unstrained lattice constant of epitaxial layer and a0 is the lattice constant of the substrate. The other strain in the perpendicular direction z (out-of-plane strain) can be expressed
as
=C is the ratio between the elastic stiffness constant. The strain is due to the combination of a hydrostatic (isotropic) stress and a uniaxial (anisotropic) stress. The hydrostatic strain causes the conduction band to shift by an amount given by:
c(hy)
ΔE = - ac(εxx+εyy +εzz)= - 2ac(1 -Cr)ε
a C
(A.3a) where is the conduction-band deformation potential. The hydrostatic strain causes the valence band to shift by an amount given by:
ac
v(hy)
ΔE = - av(εxx +εyy +εzz)= - 2 v(1 - r)ε
(A.3b) where is the first deformation potential for the valence-band. The hydrostatic shifted bandgap is given by:
av
(hy) gu c(hy) v(hy)
E = E - ΔE + ΔE
(A.4) However, the actual bandgap will be a little different to E(hy) because the uniaxial strain causes the heavy-hole (hh) band and the light-hole (lh) band to separate (lifting of the degeneracy).
The non-hydrostatic shift of heavy-hole band is given by:
1 2 || (A.5) where b is the second (shear) deformation potential for valance-band. The strained bandgap can be expressed as
(c-hh) (hy) a linear interpolation (Vegard’s law) as well as Eq. (A.8) is applied to calculate them approximately according to their relevant binary semiconductor parameters in Table A-1.
1-x-y x y z 1-z
For the materials discussed here, the line up of the valance-band positions across heterojunction can be calculated according to Harrison’s model [A1]. The heavy-hole and light-hole potentials are given respectively by
H H where is presented as the unstrained Harrison’s potential of valance-band. As for bowing parameters using in calculation of , that for alloys of InGaAs and InAlAs are the only two reported ones, thus, the are estimated approximately as given below
H
where is the unstrained Harrison’s potential of conduction-band. The energy-band structure for In1-xGaxAs illustrated in Fig. A.1 according to [A3] help us to figure out the strain effect.
Notations in Fig. A.1 are somewhat different to that mentioned above like as Eg(x) is our Egu.
H
Ecu
Fig. A.1. The energy-band structure in the momentum space for a bulk In1-xGaxAs under (a) compressive, (b) lattice-matched, and (c) tensile conditions which is adopted from [A3].
A.1.4 Effective mass with strain
Under biaxial strain, the effective masses are no longer isotropic. The out-of-plane (z-direction) and in-plane (x-y directions) electron effective masses are given respectively by
* * hy
e eu
gu
m = m (E )
⊥ E 2
Out-of-plane electron effective mass (A.12a)
* * hy
e eu
gu
m = m E
E In-plane electron effective mass (A.12b) where m*eu is the electron effective mass in the unstrained material. For alloys, the electron
effective mass under unstrained condition is given by electron mass. The out-of-plane and in-plane heavy-hole and light-hole masses are inter-related through three Luttinger parameters γ1, γ2, γ3 (see Table A-1). However, most bowing factors of Luttinger parameters are still unknown; therefore, people estimate them just according to Vegard’s law. For a highly strained bulk material, the out-of-plane and in-plane heavy-hole masses are given respectively by: The out-of-plane and in-plane light-hole masses are given respectively by:
* 0
where strain-dependent factor is given by This expression presents a problem at ε = 0, because both the numerator and denominator become zero. The problem can be avoided by using the following approximative formula:
2 p
2S(1 + 1.5P + 3R) 1 - R + 1 + 2R + 9R
f = , where S =
1 + 0.75P - 3RS 4 (1 + 2R) (A.18)
For an unstrained bulk material, the hole effective masses are highly direction dependent:
* 0 * 0 To obtain a simplified isotropic model for the valence-band, one takes the spherical approximation for which The approximative isotropic hole masses are given by
* 0
Based on this model, the heavy-hole, light-hole, and conduction-band effective densities of states
where T is the temperature (K). However, in quantum wells, the in-plane effective masses
and may change significantly from one confined state to the other due to interactions among the nearby states.
*
mhh
*
mlh
A.2 Characteristics of In1-x-yGaxAlyAs strained alloys on InP
According to Vegard’s law as Eq. (A.8) and Table A-1, the unstrained lattice constant of In1-x-yGaxAlyAs can be simplified as
u 1-x-y x y 0(InAs) 0(GaAs) 0(AlAs)
a (In Ga Al As) = (1-x-y) a + x a + y a According to Eq. (A.1) and Table A-1, the unstrained bandgap of In1-x-yGaxAlyAs alloys at T = 300 (K) is simplified as
gu 1-x-y x y
2 2
E (In Ga Al As)
= 0.354(1-x-y) + 1.422x + 3.003y - 0.42(1-x-y)x - 0.70(1-x-y)y - 0.347xy - 1.44(1-x-y)xy
= 0.354 + 0.648x + 1.949y + 0.42x + 0.7y + 0.773xy - 1.44(1-x-y)xy fractions for bulk In1-x-yGaxAlyAs material system and apply Eq. (A.24) to indicate the curves relative to unstrained bandgap by assuming alloy’s in-plane strain (ε
In Fig. A.2(b), we show the strained conduction- and valance-band edge for ε|| = -2%, -1%, 0%, 1%, 2%, and 3%. Substitute Eq. (A.25) to (A.26a) and (A.26b), we show the trend of Eg vs. Al (y) for lattice-matched In1-x-yGaxAlyAs alloys in Fig. A.3(a). Comparing the bandgap Eg obtained from (A.26a) and (A.26b), their difference is more clear as Al-content (y) increased. The inconsistent bandgap is major caused by the unequally chosen Eg value of AlAs between both formulas. Eq. (A.26a) use Eg (AlAs) = 3.003 eV as indicated in Table A-1 but Eq. (A.26b) is based on Eg (AlAs) = 3.03 eV. In order to match the experimental data from [A4], Eq. (A.26b) having a higher AlAs Eg, therefore, chooses a bowing factor of -2.0 higher than that of -1.44 used in Eq. (A.26a). In Fig. A.3(b), we present the band alignment of band edge between In1-x-yGaxAlyAs (M), In0.523Al0.477As (M) and InP by Harrison’s model. Depending on Eq.
(A.26a), we observe the resultant conduction-band offset (ΔEc), valance-band offset (ΔEv), and ΔEc/ΔEg in the interface of In1-x-yGaxAlyAs (M) – In0.523Al0.477As (M) are very consistent with those experimental result referred to [A5] as shown in Fig. A.3(c). Furthermore, the relation of
|ΔEc|/ΔEg vs. Al (y) indicated in Fig. A.3(d) helps us to estimate how many Al (y) fractions will form a type-II heterojunction in the interface of In1-x-yGaxAlyAs (M) – InP. It indicates the interface will keep a type-I heterojunction until Al-content (y) is higher than 28%; however, the condition for maintaining type-I one is somewhat different to that pointed out in [A6] which is 22%. In Fig. A.4(a), a 3D diagram of inverse in-plane effective mass vs. Ga (x) and Al (y) mole fractions shows the in-plane hole effective mass is significantly increased when epitaxial layer is more compressive strained (ε|| < 0), whereas it is decreased as one is more tensile strained (ε|| >
0). In Fig. A.4(b), a y-side view from Fig. A.4(a) indicates the in-plane electron effective mass is not too much affected by the strain effect but obviously increased as the Al (y) mole fraction is increased; otherwise, the in-plane hole effective mass is only a little increased when Al (y) is increased.
Table A-1. Important bandgap structure parameters for the binary III-V material systems: InAs, GaAs, AlAs, InP, GaP, and AlP [A2], [A3].
Parameter Symbol
nit)
(u InAs GaAs AlAs InP GaP AlP
Lattice Constant a0 ( ) 6.0583 5.65325 5.6611 5.8687 5.4505 5.4672
Bandgap Eg (eV) 0.354 1.422 3.003 1.353 2.777* 3.553*
Spin-orbit split-off energy Δso 0.39 0.341 0.28 0.108 0.08 0.07 Electron effective mass me*/m0 0.026 0.0635 0.15 0.0795 0.13 0.22 Harrison’s model
Conduction band position EcH(eV) 0.795 1.533 2.5785 1.353 2.389 2.874 Valence band position EvH(eV) 0.441 0.111 -0.4245 0 -0.388 -0.679 Note: all parameters at T = 300 K
*Indirect band gap, Eg (X) value.
** Very rough estimate
Table A-2. Bowing parameters of ternary and quaternary compounds.
Elements
Parameters Value (eV) In Ga Al As P
○ ○ ○ Cg(InGaAs) 0.42
○ ○ ○ Cg(InAlAs) 0.70
○ ○ ○ Cg(GaAlAs) 0.347
○ ○ ○ Cg(InGaP) 0.65
○ ○ ○ Cg(InAlP) -0.48
○ ○ ○ Cg(InAsP) 0.1
○ ○ ○ Cg(GaAlP) 0.49
○ ○ ○ Cg(GaAsP) 0.19
○ ○ ○ Cg(AlAsP) 0.05
○ ○ ○ ○ Dg(InGaAlAs) -1.44
○ ○ ○ ○ Dg(InGaAsP) 0.1
(a)
(b)
Fig. A.2. (a) Unstrained bandgap energy, (b) strained band edge of conduction-band (Ec, blue) and valance-band of heavy-hole (Ev(hh), red), and light-hole (Ev(lh), green) vs. Ga (x) and Al (y) mole fractions for In1-x-yGaxAlyAs material system.
Fig. A.3. (a) Bandgap, (b) Band lineup, (c) ΔEc, ΔEv, and ΔEc/ΔEg on In0.523Al0.477As (M), and (d)
|ΔEc|/ΔEg on InP vs. Al (y) mole fractions for lattice-matched In1-x-yGaxAlyAs material system.
(a)
(b)
Fig. A.4. (a) A 3D diagram for inverse in-plane effective mass of electron and hole (heavy- and light-hole) vs. Ga (x) and Al (y) mole fractions, and (b) its side-view in y direction when in-plane strain (ε||) = -2%, -1%, 0%, 1%, and 2%.
Reference
[A1] W. A. Harrison, “Elementary theory of heterojunctions,” J. Vac. Sci. Technol., vol. 14, pp.
1016-1021, 1977.
[A2] I. Vurgaftman, J. R. Meyer, and L. R. Ram-Mohan, “Band parameters for III-V compound semiconductors and their alloys,” J. Appl. Phys., vol. 89, pp. 5815-5875, 2001.
[A3] S. L. Chuang, Physics of Optoelectronic Devices (Wiley, New York, 1995).
[A4] D. Olego, T. Y. Chang, E. Silberg, E. A. Caridi, and A. Pinczuk, “Compositional dependence of band-gap energy and conduction-band effective mass of In1-x-yGaxAlyAs lattice matched to InP,” Appl. Phys. Lett., vol. 41, pp. 476-478, 1982.
[A5] X. H. Zhang, S. J. Chua, S. J. Xu, and W. J. Fan, “Band offsets at the InAlGaAs/InAlAs (001) heterostructures lattice matched to an InP substrate,” J. Appl. Phys., vol. 83, pp.
5852- 5854, 1998.
[A6] J. Bohrer, A. Krost, and D. B. Bimnerg, “Composition dependence of band gap and type of lineup in In1-x-yGaxAlyAs/InP heterostructures,” Appl. Phys. Lett., vol. 63, pp.1918-1920, 1993.
Appendix - B
Achievable Epitaxial Materials
The basic epitaxial materials used in the design of the wafers are ternary (In10.523Al10.477As, In10.532Ga10.468As) and quaternary (In10.528Ga20.26Al20.212As, Eg = 1eV) alloys lattice-matched to the InP substrate. (Note: the superscript for Group-III materials means the index of the effusion cells used in our MBE system.) Therefore, MBE system includes at least one Indium, two Ga, and two Al cells. Once the molecular fluxes of these three lattice-matched alloys are calibrated and fixed, the multi-selection of cells are used to provide various strained materials in the QW structure.
Based on these three basic lattice-matched alloys, we know FGa1
/ FIn1 cell-1 and cell-2 are used simultaneously) alloys, the mole fra tion of x and y are given by c
x a FFG
Therefore, we have another twelve strained materials (ternary or quaternary) for QW structure design as listed in Table B-1. According to appendix-A, their important parameters have been calculated and presented in Table B-2. Band alignment diagrams according to the data in Table B-2 (part I) are also exposed in Fig. B.1.
Table B-1. Possible composition of In1-x-yGaxAlyAs alloys.
(The superscript “3” means cell-1 and cell-2 are used simultaneously)
In1-x-yGaxAlyAs
Table B-2 (part-I)
Calculated parameters of possible In1-x-yGaxAlyAs alloys based on the lattice-matched 1eV InGaAlAs.
Calculated parameters of possible In1-x-yGaxAlyAs alloys based on the lattice-matched 1eV InGaAlAs.